Feasibility of keeping Mars warm with nanoparticles

One-third of Mars’ surface has shallow-buried H2O, but it is currently too cold for use by life. Proposals to warm Mars using greenhouse gases require a large mass of ingredients that are rare on Mars’ surface. However, we show here that artificial aerosols made from materials that are readily available at Mars—for example, conductive nanorods that are ~9 micrometers long—could warm Mars >5 × 103 time smore effectively than the best gases. Such nanoparticles forward-scatter sunlight and efficiently block upwelling thermal infrared. Like the natural dust of Mars, they are swept high into Mars’ atmosphere, allowing delivery from the near-surface. For a 10-year particle lifetime, two climate models indicate that sustained release at 30 liters per second would globally warm Mars by ≳30 kelvin and start to melt the ice. Therefore, if nanoparticles can be made at scale on (or delivered to) Mars, then the barrier to warming of Mars appears to be less high than previously thought.

Supplementary Text.

Calculation of optical properties of nanorods.
Simple calculations (e.g., ref. 17) suggest that 9 µm long conductive nanorods with a 60:1 aspect ratio would have a strong and broad extinction in the ~22 µm spectral window.To test this, we carried out finite-difference time domain simulations (FDTD: 3D Electromagnetic Simulator).First, we verified that the FDTD simulations reproduce Mie theory for water ice spheres (49) (Fig. S1).The nanorod FDTD simulations use a pulse of light whose interaction with the simulated nanoparticle is Fourier-decomposed to obtain the λ -dependence of the absorption and scattering cross sections as well as the scattering asymmetry.The representation of the angular distribution of scattered light by a single parameter, the scattering asymmetry, is standard in climate modeling (e.g., 28).75 wavelengths, approximately log-uniformly spaced from 0.24-55 µm, are obtained (Table S1).We used refractive indices for Fe from Ref. 50, and for Al from Ref. 51. Ref. 52 suggest that Fe refractive indices obtained prior to their own work might be affected by Feoxidation, but as Mars' atmosphere is ~0.1% O2 some degree of oxidation is inevitable, so this is acceptable.Implementation involved combining three different simulations for different λ ranges, for computational feasibility.75 simulations were carried out for the 9 µm long nanorod, corresponding to the product of 5 orientations in θ, 5 orientations in φ (0°, 30°, 45°, 60°, and 90°, for both angles), and three λ ranges.Here, θ corresponds to rotations in the E-H plane and the other rotation is termed φ (k-E plane, symmetric and similar to k-H plane) (Fig. S2).Far-field methods were employed to obtain the scattering phase function.We anticipate that actual nanorods will have circular cross-sections.Because of computational limitations associated with the FDTD approach, we model a nanorod with square cross-section, but find that switching between circular and square cross-sections makes negligible difference to the calculated optical properties (Fig. S3).
As expected, the simulated nanorods showed strong, broad absorptions near 22 µm (Fig. 1), supporting their suitability for Mars warming.This is consistent with previous work on Ag nanorods (53).The wavelength of the absorption peak is slightly longer than double the rod length, due to plasma effects (54).In order to average over orientations (Fig. S4), rod orientation was uniformly sampled on the sphere relative to the incident electric field vector (~1000 samples between 0° and 90° for both angles) and optical properties interpolated using a spline in the grid of 25 computed orientations for each λ.The orientations of nanorods in the atmosphere are assumed to be random and uniform, hence averaging over a spherically equidistant grid of orientations would result in proper orientation-averaged characteristics.We found (minor) infrared back-scattering in these simulations.A sensitivity test using the 3D model for Fe nanorods showed that this choice makes little difference (~0.3 K) to the calculated temperatures.
To check the interpolation accuracy, we did check runs on multiple intermediate points (Fig. S5).When the rod is viewed nearly end-on, the interpolation results grow less accurate.However, endon geometries are infrequently encountered, and at the higher angles, the scattering and absorption cross-sections are substantially smaller, so the effect of these points on the overall orientation average is insignificant.To check the simulation accuracy, we did a check run increasing the resolution across the width of the nanorod from 8 simulation mesh points (20 nm spacing) to 10 simulation mesh points (16 nm spacing), finding negligible differences (Fig. S6).
We also did calculations for 7.5 µm-long Fe nanorods with cross-section 0.08 µm × 0.08 µm, finding peak extinction around 20 µm (Fig. S7), and less climate warming per nanorod, but more climate warming per kg of nanorods.An optimal warming approach might use a mix of rods of different lengths.Moreover, we find that the total extinction (absorption plus scattering) for Al nanorods is the same as for Fe nanorods (Fig. S8), and the corresponding warming is also about the same (Table S2), even though the density of Al is three times less than that of Fe.Fe, Al, and Mg are all present at >4 wt% level in Mars soil.We focus here on Al and Fe because optical properties are available over the full wavelength range of interest (other metals are worthy of future investigation).This suggests that further research might yield further improvements in the effectiveness of warming.
2. Calculation of the surface-warming effect of the nanorods using 1D climate model.Our single-column radiative-convective climate model (RCM) subdivides atmospheres into multiple vertical log-layers (we implement 201 layers here) that extend from the ground to the top of the atmosphere (1 × 10 -5 bar here) (e.g.25).The RCM has 55 infrared and 38 solar spectral intervals (55).The model applies a standard moist convective adjustment (e.g.56).Should tropospheric radiative lapse rates exceed their moist adiabatic values, the model relaxes to a moist H2O adiabat at high temperatures or to a moist CO2 adiabat when temperatures are low enough for CO2 to condense.The RCM implements a standard solar spectrum (57).For present Mars (solar flux = 585 W/m 2 ), we assume a typical stratospheric temperature of 155 K and a surface albedo of 0.22 (e.g.24).The atmospheric pressure is a Mars-like 650 Pa with an assumed acceleration due to gravity of 3.73 m/s 2 .Although we prescribe a tropospheric relative humidity of 50%, our results are insensitive to this parameter.The baseline mean surface temperature of the resultant pure CO2 atmosphere (without nanorods) is 218 K.For comparison, Mars' observed global mean surface temperature is 202 K (10).The 1D model runs warmer in the 6 mbar no-nanorods case mainly because it lacks day-night and equator-pole temperature contrast, and because it lacks clouds, dust and topography (10).With an assumed surface albedo of 0.22 and solar flux of 585 W/m 2 , the predicted equilibrium temperature (Teq) would be ~212 K (assuming a perfect blackbody).This 212 K Teq value is the minimum surface temperature for a 1D model with no greenhouse effect.However, our 1D model predicts 6 K greenhouse effect (consistent with data and with other models), raising the mean surface temperature to ~218 K (e.g.58).In summary, the warm 1D model output gives a useful benchmark comparison on the importance of 3D factors like dust, clouds and topography on modeling predictions in comparison with that from the nanorods.
One of the reasons for the differences in temperature response between the models is the baseline surface temperature, which is higher in the 1D model (for reasons explained above).The main cause, however, is differences in the vertical temperature profiles across models (e.g., Fig. S18).For instance, lapse rates differ slightly (the top of the cloud deck is at a slightly higher pressure level, or closer to the ground, in the 3D model) and the 3D model has a near-surface temperature inversion which is absent in the 1D code (Fig. S18).The 3D model also has a larger effective convective region.Tests confirm that the 1D and 3D results agree more closely when the 3D profile is imposed on the 1D model.For example, at τFe = 0.25, imposing the same mean surface temperature in the 1D model as is obtained for the 3D model (~225.5 K) yields a top-of atmosphere (TOA) net outgoing longwave radiation/net incident stellar flux ratio of ~0.69 (a value equal to 1 corresponds to a TOA radiative equilibrium).In other words, the 1D model "wants" to warm.However, when the 3D model vertical temperature profile was applied instead (at the same surface temperature), this ratio had increased to 0.86 (removing ~60% of the difference from 1).In other words, most of the difference between the 3D model and the 1D model can be explained by differences in the vertical thermal profile.This suggests that even across 3D models, differences in convective schemes (and temperature profiles) could produce some spread in the results, motivating investigation of engineered warming of Mars using different 3D schemes.Despite these numerical differences, the atmospheric response to nanorod addition in both the 1D and 3D models is qualitatively very similar.In both cases, nanoparticle warming provides a greenhouse effect >5,000× greater than the current state of the art.Following Refs.24-25, we calculate the wavenumber-dependent optical depths (τ) for the nanorods from the following expression: Here, NRC is the nanorod content (g/m 3 ) and Δz is the path length.This equation differs from (1) only in that the optical depth is integrated over all nanorod heights and across all wavenumbers, not just in the spectral window.The nanorods are well-mixed throughout the atmosphere (up to 35 km) above the imposed 500 Pa nanorod-layer base and so NRC was assumed to scale linearly with the local pressure.We computed the radius of the sphere with the equivalent nanorod volume, which yields an effective nanorod particle radius of ~0.38 µm for the 9 µm nanorods.
Within the 1D model framework, we implement a simple procedure to calculate nanorod warming.For each assumed nanorod optical depth, we find the surface temperature that yields stratospheric energy balance (i.e. the net outgoing and net incoming fluxes must balance each other) (Figs.S16-S17).

Calculation of the surface-warming effect of the nanorods using 3D climate model.
The FDTD output is interpolated to 2000 log-uniformly spaced λ's.We set optical properties at λ >55 µm equal to those at 55 µm (Fig. S9).This approximation is acceptable, because extinction (W/m 2 /µm) is minor at such long λ.MarsWRF uses a two-stream radiation code (e.g.22,59).Radiative transfer calculations include both gas (for this work, CO2) and aerosol (for this work, natural dust, nanorods, and CO2 ice) radiative effects.This implementation of MarsWRF uses Planck-weighted averaging to bin down high-spectral-resolution optical properties.The blackbody temperature used for the Planck-weighted averaging is 6000 K for solar bands (6 bins from 0.24-4.5 µm, with bin edges at 0.24, 0.40, 0.8, 1.31, 1.86, 2.48, 3.24, and 4.5 µm), and 215 K for the thermal infrared bands (6 bins from 4.5-1000 µm, with bin edges at 4.5, 8.0, 12.0, 14.1, 16.0, 24.0, 60, and 1000 µm) (Fig. S9).Thermal equilibrium between gas and dust is assumed.We neglect radiation pressure, magnetic effects, quantum size effects, and temperature dependence of the optical constants.
In the fixed-cloud runs, present-day Mars values are used for orbital parameters, surface albedo, and surface thermal inertia.Mars' southern summer solstice occurs near perihelion, so (by Kepler's second law) northern summer is long and relatively cool, and southern summer is short and warm relative to annual average (Figs.S10-S12).Water vapor abundance in the atmosphere is fixed to zero, which is conservative in that water vapor radiative feedback would increase warming.A prescribed natural dust aerosol distribution is imposed corresponding to the Mars Climate Database MGS-dust-scenario (60), giving an average dust optical depth of 0.20 (peaking at 0.43 during southern summer).Natural dust aerosol warms the atmosphere but lowers daytime surface temperature.The artificial-aerosol layer is parameterized by a layer-base pressure (in Pa), a layer vertical thickness (in units of model levels), and the nanorod orientation-averaged optical depth at a reference λ (0.67 µm).Because the model levels are specified in η coordinates (where η = P/Psurf, where the model-top pressure has been subtracted from both pressures), the aerosol layer is physically more compact over the poles because low temperatures compact the air column.We refer to the altitude away from the poles below which 95% of the particles are contained as the "aerosol layer top height".The nanorod mixing ratio is assumed to be uniform within the nanorod layer (Fig. S13).We prescribe a layer-base level of 500 Pa and vary the layer thickness.This approach gives a maximum in artificial-aerosol opacity above the surface, which is also observed for natural Mars dust aerosol for some seasons (61)(62)(63).However, natural dust on Mars persists all the way to the surface (63) which has average pressure ~600 Pa.This has no effect on our conclusions, as results are only weakly sensitive to the vertical distribution of simulated aerosolfor example, in Table S3, the "Thinner cloud (200 Pa base, 8 levels)" run differs from the reference case with 500 Pa base by only 0.3 K in average temperature.Buffering by latent heat implies that melting either ice cap to form seas would take at least centuries.
Settling for a 0.1 µm-radius dust particle for 1 scale height at Mars surface pressure takes 3 years (Murphy 1990).Extrapolation to Al nanorods with radius 0.04-0.08µm suggests settling times that are similar or greater.Increase of Mars' atmospheric pCO2 under warming will decrease the Knudsen number and hinder dust settling.One-pass settling rates are much slower than that of natural Mars dust, and effective particle lifetime will be longer due to re-entrainment.
The runs presented here use a horizontal resolution of 5.625° × 3.75°, corresponding to a grid of 64 points in longitude × 48 points in latitude.A 40-layer vertical grid is used, using a modified-η (terrain-following) coordinate (η = P/Psurf, where the model-top pressure has been subtracted from both pressures).The dynamical timestep varies between runs but is never longer than 1-min.The planetary boundary layer scheme is based on that in Ref. 64 (Medium-Range Forecast model scheme), with Mars implementation similar to that in Ref. 20, and the surface layer uses a Monin-Obukhov scheme.Runs are initialized from a cold state and continue until the simulated annual seasonal cycle is highly repeatable from year to year.We found that runs require only a single year of spin-up adjustment, as modern Mars, lacking seas, has low effective thermal inertia.Output is reported from the third year of each model run.Mean wind speed ~30 m above the surface increases from 8 m/s in the no-nanorods case to 13 m/s in the Fig. 2a (with-nanorods) case, which would stir up more dust (and nanorods).Daytime near-surface turbulence on Mars is sufficient to loft dust (and therefore nanorods) released at 10-100m altitude at all latitudes for P > 6 mbar.Sensitivity tests adjusting model resolution, and varying nanorod distribution and other parameters are listed in Table S3.
For the no-nanorods case (Fig. 2b), the global and annual average shortwave radiation reaching the surface is 133.1 W/m 2 (119.7 W/m 2 direct beam and the remainder diffuse/scattered), of which 104.2 W/m 2 is absorbed with the rest being reflected.The spatially-and time-averaged surface albedo, including ice, is 0.237.The global/annual average longwave radiation at the surface (greenhouse effect) is 23.9 W/m 2 .The global/annual average longwave emission from the surface is 125.4W/m 2 .The mismatch of -2.7 W/m 2 is caused by limited output sampling, fluxes into the surface (e.g.CO2 condensation, conduction), and model imprecision.For the with-nanorods case shown in Fig. 2a, the global and annual average shortwave radiation reaching the surface is 89.2 W/m 2 (41.4 W/m 2 direct beam), of which 70.6 W/m 2 is absorbed with the rest being reflected.The spatially-and time-averaged surface albedo, including ice, is 0.208.A greater fraction of sunlight is absorbed due to reduction in reflective seasonal CO2 ice.The global/annual average longwave radiation at the surface (greenhouse effect) is 186.2W/m 2 .The global/annual average longwave emission from the surface is 254.3W/m 2 .The mismatch of -2.5 W/m 2 (i.e., surface temperature under-stated relative to radiative fluxes) is caused by limited output sampling, fluxes into the surface (e.g.CO2 condensation, conduction), and model imprecision.
The runs shown in Fig. 2c correspond to optical depths at λ = 0.67 µm of {0, 0.125, 0.25, 0.5, 0.75, 1, 1.5, 2}.Details for selected values are given in Fig. S14.The conversion factor is 545 mg/m 2 for Fe and 212 mg/m 2 for Al for one optical depth.Optical depths in the spectral windows are much greater than at 0.67 µm (Fig. 1).Output was sampled at 260 equally spaced intervals per Mars year.This provides (deliberately aliased) sampling of the day-night cycle during each season at each longitude and latitude.A sensitivity test using 1300 output steps showed negligible (≤0.1 K) differences in both annual-average and seasonal warming (Table S3).Mars' atmosphere is thin, with low thermal inertia and limited ability to transport heat laterally, and the tests with artificial imposed patchy or unsteady nanorod distribution show that the corresponding warming is sharply confined in space and time.This suggests that it might be possible to enhance warming at preferred latitudes and seasons.The atmosphere and surface temperature quickly responds to the radiative forcing at the release site/time, and after injection ceases, spreading of the particles away from the release site ensures that the warming at the release site soon decreases.

Possible hazards.
Natural Mars air is unsafe for humans to breathe because it has almost no oxygen (insufficient for deflagration) and also has a high natural concentration of PM 2.5 (Mars mineral aerosol dust).The nanorod density is ~10 µg/m 3 , which would not substantially alter this situation.A more immediate concern is asbestosis, as humans would bring both natural dust and nanoparticles into settlements via airlocks.One way to mitigate this hazard would be to make nanorods that dissolve or fragment in liquid water.

Comparison to previous work.
To our knowledge, the most effective (on a per-unit-mass-in-the-atmosphere basis) Mars warming agent that has been previously been proposed is the "optimal [gas] mix" of ref. 8, which is mostly C3F8 (molecular mass 188 Da).This gives 37.5 K warming for 1 Pa, which corresponds to 170 kg/m 2 × (1 Pa / 650 Pa) × (~188 Da / 44 Da) ≈ 1.1 kg/m 2 .This warming is about the same as the nanorod case shown in Fig. 2a, which corresponds to ~160 mg/m 2 of Al nanorods.Therefore this nanorod loading (using non-optimized nanoparticles) is >5000× more effective than the optimal gas mix.Fig. S8.Showing the calculated optical properties varying particle length and width for the same particle composition: specifically, 7.5 µm-long Fe nanorods with cross-section 0.08 µm × 0.08 µm, compared to 9 µm-long Fe nanorods with cross-section 0.16 µm × 0.16 µm.Orientation-averaged optical properties calculated using a 3D Finite-Difference Time-Domain (FDTD) approach.Upper panel: Solid black line corresponds to total extinction, dotted black line to scattering, both for 7.5 µm-long Fe nanorods with cross-section 0.08 µm × 0.08 µm.Lower panel shows scattering asymmetry.Also shown in both panels are spectra for natural dust assuming a log-gaussian particle size distribution centered on 2.5 µm (48) (red dotted lines).In both panels, gray lines correspond to the results for a 9 μm-long Fe nanorod with cross-section 0.16 µm × 0.16 µm.As expected given its spectrum, the 7.5 µmlong nanorod gives ~2× less warming per nanorod in climate simulations.However, as it uses 5× less Fe, this design is more effective on a warming-per-unit-mass basis.S19).The purple shading corresponds to the relative volume density of nanorods.The mixing ratio of nanorods within the purple layer is uniform, but there is more gas closer to the planet's surface so there are also more nanorods lower down.The tenuous part of the nanorod layer extending to high altitude is disproportionately important because of its strong contribution to the greenhouse effect.The Y-axis uses terrain-following η-coordinates (η = P/Psurf, where the model-top pressure has been subtracted from both pressures), and the cloud lines are tilted down and to the left because the southern hemisphere surface is topographically higher and thus closer to the fixed-pressure base of the nanorod layer.The yellow lines are contours of annual average atmospheric temperature.The green lines are contours of altitude in meters, which bow upwards at the poles where low temperatures compact the gas column.

Fig. S1 .
Fig. S1.(a,b,c) Verification of calculations by comparison to Mie-theory results for a water-ice sphere (49), showing single particle albedo, scattering asymmetry, and extinction efficiency.(d,e) Shows the comparison of analytical Mie scattering results for an ice sphere with simulation outputs.

Fig. S2 .
Fig. S2.Illustration showing the definition of the angles θ and φ in the FDTD calculation."k" corresponds to the direction of the propagation of the incident electromagnetic wave.The gray bar corresponds to the nanorod.

Fig. S7 .
Fig. S7.Showing sensitivity of calculated optical properties to changing nanorod composition (Al vs. Fe), for a 9 µm-long, ~60:1 aspect ratio nanorod.The total extinction cross section (scattering plus absorption) and the location of the resonances remains about the same; a small increase in Al nanorod length would be sufficient to closely match the Fe cross-sections.As Al is 3× less dense than Fe, this suggests Al is more effective on a warming-per-unit-mass basis.Conductive-nanorod size and shape, and not composition, are the main controls on simulated nanorod optical properties.Aluminum material properties are obtained from ref. 51.Orientation: θ = 45°, φ = 45°.

Fig. S9 .
Fig. S9.Showing how the spectra are represented within the 3-D climate model.9 µm-long, ~60:1 aspect ratio nanorod.4.5 µm marks the separation between solar bins (Planck-weighted using the orange 6000 K blackbody curve, normalized W/m 2 /µm flux density), and thermal IR bins (Planckweighted using the pink 215 K blackbody curve, normalized W/m 2 /µm flux density).The relative heights of the orange and pink Planck functions are to guide the eye only and have no physical significance.

Fig. S11 .
Fig. S11.Seasonal variation of diurnal-average surface temperature (K) for (left) control simulation without nanorods (i.e., Fig. 2b), and (right) warmed case with ~160 mg/m 2 nanorods (i.e., Fig. 2a), showing longitudinal average surface temperature.Each of the 10 increments on the x-axis, which are equally spaced in time, corresponds to 1/10 of a Mars year (69 Earth days).To make this figure, a 9-point smoother has been used (3 points in time, and 3 points in latitude) in order to damp oscillations associated with aliasing in the sampling of the day-night temperature cycle in the output.The black lines show the limit of substantial polar seasonal CO2 ice.

Fig. S13 .
Fig. S13.Cross section of steady (imposed) nanorod layer (τFe = 0.75, Fig.S19).The purple shading corresponds to the relative volume density of nanorods.The mixing ratio of nanorods within the purple layer is uniform, but there is more gas closer to the planet's surface so there are also more nanorods lower down.The tenuous part of the nanorod layer extending to high altitude is disproportionately important because of its strong contribution to the greenhouse effect.The Y-axis uses terrain-following η-coordinates (η = P/Psurf, where the model-top pressure has been subtracted from both pressures), and the cloud lines are tilted down and to the left because the southern hemisphere surface is topographically higher and thus closer to the fixed-pressure base of the nanorod layer.The yellow lines are contours of annual average atmospheric temperature.The green lines are contours of altitude in meters, which bow upwards at the poles where low temperatures compact the gas column.

Fig. S14 .
Fig. S14.Summary of the latitudinal and seasonal dependence of surface temperature for (red lines) the 3D model with-nanorods τFe = 0.75 case (Fig. S19a), and (blue lines) the 3D model without nanorods (Fig. S19b).Solid line corresponds to the average temperature during the warmest season (~70 day period) during the year, dotted line corresponds to the average temperature during the coldest season (~70 day period) of the year, and dashed line corresponds to the annual average.The flattening-out of the lines around 145 K corresponds to buffering at the frost point of CO2.

Fig. S15 .
Fig. S15.As Fig 2c, but with a linear x-axis instead of a logarithmic x-axis.Dependence of planet-averaged surface warming on nanorod column mass.Blue triangle corresponds to Fig. 2a, the intersection of the blue line with the zero-nanorods axis corresponds to Fig. 2b, and white triangle marks onset of warm-season temperatures above the freezing point of water at 50°S.Blue corresponds to 3-D results.The blue envelope corresponds to the modeled seasonal range in global mean Tsurf.Gray corresponds to 1-D results.The red asterisk corresponds to the observed modern Mars value.

Fig. S18 .
Fig. S18.1D model vs. 3D (MarsWRF) model temperature profile comparison for τFe = 0.75.The 3D result is the global and annual average.At this optical depth, surface temperature for both models is ~ 250 K.
Fig. S19.As Fig. 2, but for 400 mg/m 2 loading of Fe nanorods instead of 160 mg/m 2 loading of Al nanorods.Warmseason temperatures (K) (color shading) on (a) Mars with addition of ~400 mg/m 2 of nanorods, (b) control case.This corresponds to the average surface temperature during the warmest 36° of solar longitude (~70 days) of the year.White contour corresponds to 610 Pa (~6 mbar) mean pressure level.Black contours correspond to topographic elevation in m (dashed: -5 km and -2 km, solid: 0 km, +2km, and +5 km).Blue lines: approximate latitudinal (equatorward) extent of ice at <1 m depths.Results do not include CO2 outgassing from within polar ice, which would cause further warming.(c) Dependence of planet-averaged surface warming on nanorod column mass.Blue line corresponds to 3-D results, varying layer-top height between ~35 km (solid line) and ~28 km (dashed line).The blue envelope corresponds to the modeled seasonal range in global mean Tsurf.Gray corresponds to 1-D results (see text for details).Blue triangle corresponds to panel (a), and white triangle marks onset of warm-season temperatures above the freezing point of water at 50°S.Symbols on y-axis are temperatures for the no-nanorod case, with the red asterisk corresponding to observed Mars value.More detail is shown in Figs.S10-S17.

Table 1 :
Orientation-averaged optical properties of nanorods as used in the climate simulations, corresponding to a 9 µm-long nanorod with cross-section (0.16×0.16) µm.

Table 2 .
Summary of climate model output.The nanorod column mass differs between the Al and Fe cases by a factor of 2.57 (ratio of material densities, corrected for the 13% greater extinction cross-section of Fe rods at 0.67 µm relative to Al rods).

Table 3 .
Summary output for additional sensitivity tests using 3D model.All were carried out using Fe nanorods.